THE RECURSIVE SOLUTION OF QUEUE LENGTH FOR Geo/G/1 QUEUE WITH N-POLICY

This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n^-,n^+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n^-,n^+,n and departure epoch D_n).

RELIABILITY INDICES OF DISCRETE-TIME Geo^X/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS

这篇论文从可靠性研究的观点与不可靠的加油站和多重适应推迟的假期认为排队的分离时间的 GeoX/G/1 是模型。后面的问题将被讨论：1 ) 服务者在在时间 n 的一个概括忙时期的概率；2 ) 加油站在在时间 n 的失败的概率，即，加油站的短暂 unavailability，和加油站的稳定的州的 unavailability；3 ) 加油站失败的期望的数字在时间间隔期间(0， n ] ，并且加油站的稳定的州的失败频率；4 ) 加油站故障在的期望的数字一概括的服务者忙碌时期。最后，作者证明有不可靠的加油站的一些普通分离时间的排队模型是在这篇论文讨论的模型的特殊情况。

Geom/G_1,G_2/1/1 REPAIRABLE ERLANG LOSS SYSTEM WITH CATASTROPHE AND SECOND OPTIONAL SERVICE

这份报纸学习一个单身的服务器有 Bernoulli 到达过程和没有等待的空格的分离时间的厄兰损失系统。在系统的服务者被假定提供服务的二种不同类型，也就是必要、可选的服务，到顾客。在系统的操作期间，大祸的到达将毁坏系统并且同时劝诱顾客立即离开系统。用一种新类型分离增补可变技术，作者获得排队系统的一些性能特征包括不变的可获得性和系统的失败频率，为是闲散的服务器，的不变的可能性忙碌，故障和系统等等的损失概率。由数字例子，最后，作者在几项表演措施上学习系统参数的影响。

ON THE TRANSIENT DEPARTURE PROCESS OF M^x/G/1 QUEUEING SYSTEM WITH SINGLE SERVER VACATION

这篇论文学习 M 的短暂离开过程[x ] 有单身的服务者假期的 /G/1 排队系统。我们在场导出从任何起始的状态发生在有限时间间隔的离开的期望的数字的一个简单概率分解方法；期望的数字的 asymptotic 扩大。特别，我们为一些特殊情况导出一些更实际的结果。

TRANSIENT QUEUE SIZE DISTRIBUTION SOLUTION OF GEOM/G/1 QUEUE WITH FEEDBACK-A RECURSIVE METHOD

This paper considers the Geom/G/1 queueing model with feedback according to a latearrival system with delayed access (LASDA).Using recursive method,this paper studies the transientproperty of the queue size from the initial state N(0^+)=i.Some new results about the recursiveexpression of the transient queue size distribution at any epoch n^+ and the recursive formulae of theequilibrium distribution are obtained.Furthermore,the recursive formulae of the equilibrium queuesize distribution at epoch n,and n are obtained,too.The important relations between stationaryqueue size distributions at different epochs are discovered (being different from the relations given inM/G/1 queueing system).The model discussed in this paper can be widely applied in all kinds ofcommunications and computer network.

Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N, D)-Policy

In this paper we consider a discrete-time Geo/G/1 queue with delayed Min(N, D)-policy.Using renewal process theory, total probability decomposition technique and z-transform, we study the transient and equilibrium properties of the queue length from an arbitrary initial state, and obtain both the recursive expressions of the transient state queue length distribution and the steady state queue length distribution at arbitrary time epoch n+. Furthermore, we derive the important relations between equilibrium queue length distributions at different time epochs n-, n and n+. Finally, we give some numerical examples about capacity decision in queueing systems to demonstrate the application of the analytical results reported in this paper.

Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period

This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service.We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution.Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.

Analysis of an k-out-of-n:G system with redundant dependency and repair equipment procurement

This paper studies an k-out-of-n:G system with redundant dependency and repair equipment procurement lead time where the operating times and repair times of components follow exponential distributions and phase-type distributions,respectively.When one component breaks down,it is repaired by a repair equipment.The repair equipment may fail during the repair period and the following repair is not‘as good as new’.After a number of repairs,it is replaced by a new one.The new spare repair equipment for replacement is only available by an order,and the procurement lead time for delivering follows a phase-type distribution.Moreover,in the multi-component system,the redundant dependency is taken into account.Applying the matrix-analytical method,the system availability,the rate of occurrence of failures of the system,the expected number of broken components,the availability and the rate of occurrence of failures of the repair equipment are derived.Finally,numerical examples are given to show these theoretical results.